Respuesta :
Answer:
Part 1) see the explanation
Part 2) see the explanation
Part 3) see the explanation
Part 4) see the explanation
Step-by-step explanation:
The question in English is
Read the situations and do the following with each one:
Write down the magnitudes involved
Write which magnitude is the independent variable and which is the dependent variable
It represents the function that describes the situation
SITUATIONS:
1) A machine prints 840 pages every 30 minutes.
2) An elevator takes 6 seconds to go up two floors.
3) A company rents a car at S/ 480 for 12 days.
4) 10 kilograms of papaya cost S/ 35
Part 1) we have
A machine prints 840 pages every 30 minutes
Let
x ----> the time in minutes (represent the variable independent or input value)
y ---> the number of pages that the machine print (represent the dependent variable or output value)
Remember that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In this problem
we have a a proportional variation
so
The value of the constant of proportionality is equal to
[tex]k=\frac{y}{x}[/tex]
we have
[tex]y=840\ pages\\x=30\ minutes[/tex]
substitute
[tex]k=\frac{840}{30}=28\ pages/minute[/tex]
The linear equation is
[tex]y=28x[/tex]
Part 2) we have
An elevator takes 6 seconds to go up two floors.
Let
x ----> the time in seconds (represent the variable independent or input value)
y ---> the number of floors (represent the dependent variable or output value)
Remember that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In this problem
we have a a proportional variation
so
The value of the constant of proportionality is equal to
[tex]k=\frac{y}{x}[/tex]
we have
[tex]y=2\ floors\\x=6\ seconds[/tex]
substitute
[tex]k=\frac{2}{6}=\frac{1}{3}\ floors/second[/tex]
The linear equation is
[tex]y=\frac{1}{3}x[/tex]
Part 3) we have
A company rents a car at S/ 480 for 12 days.
Let
x ----> the number of days (represent the variable independent or input value)
y ---> the cost of rent a car (represent the dependent variable or output value)
Remember that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In this problem
we have a a proportional variation
so
The value of the constant of proportionality is equal to
[tex]k=\frac{y}{x}[/tex]
we have
[tex]y=\$480\\x=12\ days[/tex]
substitute
[tex]k=\frac{480}{12}=\$40\ per\ day[/tex]
The linear equation is
[tex]y=40x[/tex]
Part 4) we have
10 kilograms of papaya cost S/ 35
Let
x ----> the kilograms of papaya (represent the variable independent or input value)
y ---> the cost (represent the dependent variable or output value)
Remember that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In this problem
we have a a proportional variation
so
The value of the constant of proportionality is equal to
[tex]k=\frac{y}{x}[/tex]
we have
[tex]y=\$35\\x=10\ kg[/tex]
substitute
[tex]k=\frac{35}{10}=\$3.5\ per\ kg[/tex]
The linear equation is
[tex]y=3.5x[/tex]
